🧮 algebra

1. **State the problem:** We need to find what percentage of the total prison population are men. 2. **Identify the given data:**

1. **State the problem:** Given the table of values for $x$ and $y$, find the relationship or function that connects $x$ and $y$. 2. **Observe the data:** The table shows:

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find an equation that describes the relation between $x$ and $y$.

1. **State the problem:** We want to understand why the variable $x$, representing the side length of squares cut from each corner of a 30 cm by 20 cm cardboard, must be less than

1. **State the problem:** Solve the equation $$4(x+10) = 10x$$ for $$x$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses.

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{4} - \frac{x}{5} = \frac{7}{20}.$$\n\n2. **Use a common denominator:** The denominators are 4, 5, and 20. The lea

1. **Problem statement:** Find the 50th term of the sequence 5, 8, 13, 20, ... 2. **Identify the pattern:** The sequence is not arithmetic (difference between terms is not constant

1. The problem: Understand the discriminant rules for quadratic equations. 2. The quadratic equation is generally written as $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are const

1. **Problem (a): Express $16x^2 - 24x + 10$ in the form $(4x + a)^2 + b$.** 2. Start with the expression:

1. **State the problem:** We have an arithmetic sequence with the first three terms: 7, 5, and $1 - 3x$. We need to find the value of $x$ and the next term in the sequence. 2. **Re

1. **Problem Statement:** We have two ellipses on a Cartesian plane: one gray ellipse representing a function $f(x)$ and one black ellipse representing a function $g(x)$. The black

1. **Stating the problem:** We need to find the sum of the fractions $\frac{3}{25} + \frac{1}{2} + \frac{7}{10} + \frac{3}{5} + \frac{11}{50}$.\n\n2. **Find a common denominator:**

1. **State the problem:** We need to find the slope of the highlighted line segment on the graph, which represents the helicopter descending at a constant rate. 2. **Recall the slo

1. **State the problem:** We are given the equation $8d + 1 = -8$ and asked to analyze the related equation $10c - 3 = 8$. 2. **Solve for $d$ in the first equation:**

1. The problem is to find the domain of a function, which means determining all possible input values ($x$) for which the function is defined. 2. The domain depends on the type of

1. **State the problem:** Simplify the function $f(x) = \frac{x^{3} + 2x^{2}}{x^{2} - 1}$. 2. **Recall the formula and rules:** To simplify a rational function, factor numerator an

1. The problem is to simplify the expression or equation given by the user. 2. Since the user did not provide a specific expression, I cannot simplify anything without the original

1. Find the 16th term of the sequence 9, 16, 23, 30. The sequence is arithmetic with first term $a_1=9$ and common difference $d=16-9=7$.

1. **State the problem:** We need to find the 20th term of an arithmetic sequence where the 3rd term is 19.6 and the 7th term is 48.8. 2. **Recall the formula for the nth term of a

1. The problem is to simplify the fraction $\frac{2}{4}$. 2. The formula for simplifying fractions is to divide the numerator and denominator by their greatest common divisor (GCD)

1. **State the problem:** Simplify the expressions and determine which can be simplified to $a^6$. 2. **Recall the laws of exponents:**